A084597 Largest k such that there are exactly n primes between k^2 and (k+1)^2.

5, 9, 14, 17, 23, 26, 30, 42, 49, 55, 56, 80, 77, 72, 85, 84, 89, 119, 102, 118, 137, 136, 143, 140, 149, 156, 174, 178, 188, 184, 194, 200, 195, 207, 219, 198, 228, 247, 261, 263, 245, 249, 279, 297, 289, 327, 306, 310, 325, 335, 321, 290, 356, 344, 425, 365

Offset: 2

Author

Harry J. Smith, May 31 2003

Keywords

• nonn

Comments

a(n) is the index of last occurrence of n in A014085. This sequence relies on a heuristic calculation and there is no proof that it is correct. Conjecture: There is no k that has only one prime between k^2 and (k+1)^2.

Examples

			a(14)=77 because 14 is in sequence A014085 for the last time at item 77. There are 14 primes between 77^2 and 78^2.
		

References

• P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 143.

Links

• T. D. Noe, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Landau's Problems.

Crossrefs

Cf. A007491, A014085, A076957, A084596.